MC ▸ NA ▸ courses ▸ NUMA12 – Spring 2012

In short

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Monday 15-17 in MH:333
Wednesday 10-12 in MH:332B (on 13/2 we have another room)
(MH=Mathematics house)

Thematic Schedule

DateLectureProtocol
2013-01-23

Concept of best approximation, norms.

Lecture 1
2013-01-28

Uniqueness of best approximations, the best approximation operator. Continuity. The 1-, 2- and inf- norms.

Lecture 2
2013-01-30

The Lebesgue constant. Piecewise polynomial approximations.

Lecture 3
2013-02-04

Lagrange interpolation. Interpolation error. Chebyshev polynomials. The Lebesgue constant of the Lagrange interpolation operator.

Lecture 4
2013-02-05

Reading assignment: Divided differences. The Newton form. Hermite interpolation.

The Weierstrass theorem. Monotone operators. The Bernstein operator.

Lecture 5
2013-02-11

Minimax Approximation, Haar spaces, Characterization Theorem.

Lecture 6
2013-02-13

Uniqueness of the minimax approximation. Bounds on the minimax error. Introduction to the exchange algorithm.

Lecture 7
2013-02-18

The exchange algorithm.

Lecture 8
2013-02-20

Convergence of the exchange algorithm.

Lecture 9
2013-02-25

Least squares approximation

Lecture 10
2013-02-27

Orthogonal polynomials.

Lecture 11
2013-03-04

The best L1 approximation.

Lecture 12
2013-03-06

Discrete L1 approximation.

Lecture 13